April 10, 2003

Notes: Risk Aversion

Teaching Notes for Econ 236: April 9: What do different risk aversion parameters imply about gambles?

Kocherlakota (1995) [Narayana R Kocherlakota (1995), "The Equity Premium: Its Still a Puzzle," Journal of Economic Literature, 1996-1, pp. 42-72.] reports that the raw "equity premium puzzle" implies a coefficient of relative risk aversion of 18... (and then there is the risk-free rate puzzle: at a crra of 18, you need a raw time preference factor of -8% per year to fit average per-capita consumption growth to the average real risk-free rate of interest.

What does such a high risk aversion parameter mean? Well...

...At a coefficient of relative risk aversion of 1... you are indifferent between a this year's consumption level of $30,000 for certain and a 58% chance of $40,000 coupled with a 42% chance of $20,000.

...At a coefficient of relative risk aversion of 5... you are indifferent between a this year's consumption level of $30,000 for certain and a 86% chance of $40,000 coupled with a 14% chance of $20,000.

...At a coefficient of relative risk aversion of 10... you are indifferent between a this year's consumption level of $30,000 for certain and a 97.6% chance of $40,000 coupled with a 2.4% chance of $20,000.

...At a coefficient of relative risk aversion of 20... you are indifferent between a this year's consumption level of $30,000 for certain and a 99.96% chance of $40,000 coupled with a 0.04% chance of $20,000.

Maybe I don't understand. This seems like a very small part of the story.

Many people delight at the idea of throwing money into slot machines, for which they are certain to lose in the long run.

Likewise, many people are frightened travel to China because of SARS. If SARS has infected 1200 Chinese and there are 1.2 billion of the same then isn't that a 1 in 1,000,000 chance of catching the disease? (Or a 1 in 20,000,000 chance of dying from it?)

It seems that the only way to determine an effective risk aversion parameter is to isolate it from so many factors as to make it relatively ineffective in gauging real-world situations. Am I wrong?

My layman's understanding of this issue is that
stock investors demand and receive higher returns than
bond investors. This is supposed to compensate them
for the increased risks of stocks. By looking at
historical data economists can find out the actual returns
from stocks, as well as how risky they actually
turned out to be. When they do this, they find that
stocks weren't all that risky, but they provided a
big return.

How can this be? Is it like the statement says,
that people hate even the slightest hint of risk
so much that they demand a huge return in exchange?
That's what you get if you just plug in the figures
mindlessly. But there are other explanations.

Maybe stock returns were a lot higher than investors
expected. Maybe stock risks were a lot lower.
Or maybe if they did those studies again in 2003
instead of 1995, they'd find that stocks have been
riskier and provided less return in the past decade
than was the case back in 95, bringing all the figures
more into line.

My guess is that investors don't believe, in their
guts, that things are going to go as smoothly in
the next few decades as they have in the last few.
I think people perceive a great deal
of risk going forward. Basically we've gotten lucky,
nothing that bad has happened (at least not by 1995).
Investors were more pessimistic than the reality turned
out to be. It doesn't mean that they are going to say,
oh, we learned our lesson, we'll put on our rose colored
glasses from now on. No, they still figure that there are
all kinds of problems lurking ahead. That's why they
demand a high risk premium, because they see plenty of risk.